There are no shortage of modeling methods and techniques out there for statistical analysts to utilize when working with data. Sometimes, it can be helpful to have a resource to look at and compare the value of a modeling method based on available data and the type of information an individual is interested in pulling from a dataset.

In this regard, I have curated a list of statistical techniques that can be used and when to use them. Eventually, a follow up article will be provided that discusses which packages in python can be used to easily access and deploy these techniques as well. Enjoy!

*Regression*

1. Linear Regression:

– Summary: Linear regression models the relationship between a dependent variable and one or more independent variables using a linear equation. It’s used when you want to predict a continuous target variable based on linear relationships with one or more predictors.

-When to use: Use linear regression when you have a clear linear relationship between the target variable and predictor(s) and assumptions of linearity, independence, and constant variance are met.

2. Multiple Linear Regression:

– Summary: Multiple linear regression extends linear regression to multiple independent variables, allowing you to model more complex relationships. It’s useful when you have multiple predictors influencing the dependent variable.

– When to use: Use multiple linear regression when there are several predictors affecting the target variable, and you want to assess their combined impact.

3. Polynomial Regression:

– Summary: Polynomial regression models relationships by fitting a polynomial equation to the data. It’s employed when the relationship between the variables is nonlinear and can be approximated by a polynomial curve.

– When to use: Use polynomial regression when a simple linear model doesn’t capture the underlying relationship between the variables, and you suspect a curved pattern.

4. Ridge Regression:

– Summary: Ridge regression is a regularized linear regression technique that adds a penalty term to the linear regression cost function. It’s useful when dealing with multicollinearity (highly correlated predictors) to prevent overfitting.

– When to use: Use ridge regression when you have multicollinearity issues and want to reduce the impact of highly correlated predictors in your model.

5. Lasso Regression:

– Summary: Lasso regression is another regularized linear regression method that adds a penalty term but uses L1 regularization, which can lead to feature selection by pushing some coefficients to zero. It’s beneficial when you want to perform feature selection and reduce model complexity.

– When to use: Use lasso regression when you have many predictors and suspect that only a subset of them are truly important, or when you want a simpler, more interpretable model.

6. Elastic Net Regression:

– Summary: Elastic Net combines L1 (Lasso) and L2 (Ridge) regularization, providing a balance between feature selection and parameter shrinkage. It’s helpful when you want to handle multicollinearity and perform feature selection simultaneously.

– When to use: Use elastic net regression when you have many predictors, multicollinearity, and need both regularization benefits.

7. Logistic Regression:

– Summary: Logistic regression models the probability of a binary outcome using a logistic function. It’s used for classification tasks when the dependent variable is categorical (e.g., yes/no, spam/ham).

– When to use: Use logistic regression when you need to predict binary or multinomial outcomes and want to model the probability of class membership.

8. Support Vector Regression (SVR):

– Summary: SVR is a regression technique based on support vector machines, aiming to find a hyperplane that minimizes the deviation of data points from the predicted values. It’s suitable for tasks where traditional linear regression may not work well, and you want to capture complex relationships in the data.

– When to use: Use SVR when you have non-linear data relationships and want to capture complex patterns while controlling for model complexity.

9. Decision Tree Regression:

– Summary: Decision tree regression models the data using a tree-like structure, splitting data into branches based on predictor values and assigning target values at the leaves. It’s useful when the data has nonlinear and hierarchical patterns.

– When to use: Use decision tree regression when you suspect that the relationships between predictors and the target are nonlinear and can be represented by a tree-like structure.

10. Random Forest Regression:

– Summary: Random forest regression is an ensemble method that combines multiple decision trees to make more robust and accurate predictions. It’s effective when dealing with complex, noisy data with many predictors.

– When to use: Use random forest regression when you want to improve predictive accuracy, handle missing data, and reduce the risk of overfitting in regression tasks with many predictors.

*Correlation*

1. Pearson Correlation:

– Summary: Pearson correlation measures the linear relationship between two continuous variables, providing a value between -1 and 1. It quantifies the strength and direction of a linear association.

– When to use: Use Pearson correlation when you want to assess the strength and direction of a linear relationship between two continuous variables.

2. Spearman Rank Correlation:

– Summary: Spearman rank correlation, also known as Spearman’s rho, assesses the monotonic relationship between two variables by ranking the data points and then calculating the correlation. It is robust to outliers and non-linear relationships.

– When to use: Use Spearman rank correlation when the relationship between variables is not strictly linear, and you want to assess the monotonic association.

3. Kendall Tau Rank Correlation:

– Summary: Kendall’s tau is another rank-based correlation method that measures the strength and direction of the association between two variables based on the concordant and discordant pairs of data points. It is also robust to outliers and non-linearity.

– When to use: Use Kendall’s tau when you need a non-parametric measure of association that is sensitive to both linear and non-linear relationships and is robust to outliers.

4. Point-Biserial Correlation:

– Summary: Point-biserial correlation assesses the relationship between a binary variable (e.g., yes/no) and a continuous variable. It quantifies the strength and direction of the association between the binary outcome and the continuous predictor.

– When to use: Use point-biserial correlation when you want to measure the association between a binary outcome and a continuous predictor.

5. Phi Coefficient:

– Summary: The phi coefficient is a measure of association between two binary variables. It is equivalent to Pearson correlation when both variables are binary (0/1).

– When to use: Use the phi coefficient when you want to assess the strength and direction of association between two binary variables.

6. Cramer’s V:

– Summary: Cramer’s V is an extension of the phi coefficient for larger contingency tables. It measures the association between categorical variables and can handle tables with more than two categories.

– When to use: Use Cramer’s V when you want to measure the association between two or more categorical variables and have contingency tables with multiple categories.

7. Biserial Correlation:

– Summary: Biserial correlation measures the association between a binary variable and a continuous variable, similar to the point-biserial correlation. However, it assumes that the binary variable has an underlying continuous distribution.

– When to use: Use biserial correlation when you want to assess the relationship between a binary variable with an underlying continuous distribution and a continuous predictor.

8. Distance Correlation:

– Summary: Distance correlation is a measure of dependence between two variables that captures both linear and non-linear associations. It is based on the idea of measuring the similarity of distances between data points in high-dimensional space.

– When to use: Use distance correlation when you suspect that the relationship between two variables is not strictly linear and want a comprehensive measure of dependence.

*Analysis of Variance*

1. One-Way ANOVA:

– Summary: One-Way ANOVA is used to compare the means of three or more groups to determine if there are statistically significant differences between them. It assesses whether there is a significant variation in a single categorical independent variable.

– When to use: Use One-Way ANOVA when you have one categorical independent variable and want to compare the means of multiple groups (categories) to determine if they are significantly different.

2. Two-Way ANOVA:

– Summary: Two-Way ANOVA extends the One-Way ANOVA by allowing the analysis of two categorical independent variables simultaneously. It assesses the effects of these variables and their interaction on a continuous dependent variable.

– When to use: Use Two-Way ANOVA when you have two categorical independent variables and want to analyze their individual effects, as well as their interaction effect on a continuous dependent variable.

3. Multivariate Analysis of Variance (MANOVA):

– Summary: MANOVA is an extension of ANOVA that can handle multiple dependent variables simultaneously. It assesses whether there are significant differences in group means across multiple dependent variables.

– When to use: Use MANOVA when you have multiple dependent variables and want to determine if there are significant differences between groups across these variables, while controlling for potential correlations between them.

4. Repeated Measures ANOVA:

– Summary: Repeated Measures ANOVA is used when the same subjects are measured under multiple conditions or time points. It assesses the effects of a within-subjects independent variable on a dependent variable.

– When to use: Use Repeated Measures ANOVA when you have repeated measurements on the same subjects and want to determine if there are significant differences in the dependent variable across different conditions or time points.

5. Analysis of Covariance (ANCOVA):

– Summary: ANCOVA combines ANOVA and regression, allowing you to analyze the effect of a categorical independent variable while controlling for the influence of one or more continuous covariates. It is used to assess group differences while adjusting for potential confounding factors.

– When to use: Use ANCOVA when you want to compare group means while accounting for the influence of one or more continuous covariates that might affect the dependent variable.

6. Mixed-Design ANOVA:

– Summary: Mixed-Design ANOVA combines elements of both Two-Way ANOVA and Repeated Measures ANOVA. It is used when you have both between-subjects (categorical) and within-subjects (repeated measures) factors in your study.

– When to use: Use Mixed-Design ANOVA when you want to analyze the effects of both categorical and repeated measures factors on a continuous dependent variable.

7. Nonparametric ANOVA:

– Summary: Nonparametric ANOVA, such as the Kruskal-Wallis test, is used when the assumptions of traditional ANOVA (normality, homogeneity of variances) are not met. It tests for differences in group medians instead of means.

– When to use: Use Nonparametric ANOVA when your data violates the assumptions of traditional ANOVA and you need a robust alternative for comparing groups.

*Cluster Analysis*

1. K-Means Clustering:

– Summary: K-Means clusters data points into K distinct groups based on their similarity, with each group represented by its centroid. It’s widely used for partitioning data into non-overlapping clusters.

– When to use: Use K-Means when you have a large dataset and want to find clusters with roughly equal sizes and simple, spherical shapes.

2. Hierarchical Clustering:

– Summary: Hierarchical clustering builds a tree-like hierarchy of clusters, either agglomerative (bottom-up) or divisive (top-down). It’s used for exploring data at different granularity levels.

– When to use: Use hierarchical clustering when you want to explore the hierarchical relationships within your data and don’t have a predefined number of clusters.

3. DBSCAN (Density-Based Spatial Clustering of Applications with Noise):

– Summary: DBSCAN identifies clusters based on the density of data points, making it effective for finding clusters of varying shapes and handling noise points. It can discover arbitrary-shaped clusters.

– When to use: Use DBSCAN when you suspect that clusters in your data have irregular shapes and varying densities or when you want to automatically detect outliers.

4. Mean Shift Clustering:

– Summary: Mean Shift is a density-based clustering technique that shifts data points towards the mode of the local data density, converging on cluster centers. It’s effective for identifying clusters with varying shapes and sizes.

– When to use: Use Mean Shift when you want to find clusters with irregular shapes and varying densities, especially in computer vision and image processing tasks.

5. Agglomerative Clustering:

– Summary: Agglomerative clustering is a hierarchical method that starts with individual data points as clusters and merges them iteratively based on similarity. It’s useful when you want to explore hierarchical relationships in your data.

– When to use: Use agglomerative clustering when you’re interested in understanding the hierarchical structure of your data and the number of clusters is not predetermined.

6. Gaussian Mixture Model (GMM):

– Summary: GMM assumes that the data is generated from a mixture of Gaussian distributions. It estimates the parameters of these distributions, allowing for probabilistic assignment of data points to clusters.

– When to use: Use GMM when you believe that your data is generated from a combination of Gaussian distributions and want to model uncertainty in cluster assignments.

7. Self-Organizing Maps (SOM):

– Summary: SOM is a type of neural network that organizes data into a low-dimensional grid while preserving the topological relationships between data points. It’s useful for visualizing high-dimensional data.

– When to use: Use SOM when you want to visualize and explore the underlying structure of high-dimensional data in a lower-dimensional space.

8. Fuzzy C-Means Clustering:

– Summary: Fuzzy C-Means assigns data points to multiple clusters with varying degrees of membership, allowing data points to belong partially to multiple clusters. It’s suitable when data points can belong to multiple clusters simultaneously.

– When to use: Use Fuzzy C-Means when you want to model the uncertainty of data point assignments and allow for partial membership in multiple clusters.

*Interpolation*

1. Linear Interpolation:

– Summary: Linear interpolation estimates values between two known data points by assuming a straight-line relationship. It’s simple and suitable when the data appears to change linearly between points.

– When to use: Use linear interpolation when you have evenly spaced data points and expect a relatively linear relationship between them.

2. Polynomial Interpolation:

– Summary: Polynomial interpolation fits a polynomial function to a set of data points, allowing for more flexibility in capturing non-linear relationships. It’s used when data does not follow a linear pattern.

– When to use: Use polynomial interpolation when you need to approximate a curve or a function based on a set of data points and suspect that the relationship is polynomial in nature.

3. Spline Interpolation:

– Summary: Spline interpolation divides the data into smaller segments and fits separate polynomial functions to each segment. It provides smooth and continuous curves, making it ideal for data with abrupt changes.

– When to use: Use spline interpolation when you want to capture smooth transitions and avoid abrupt changes in your interpolated function.

4. Kriging:

– Summary: Kriging is a geostatistical interpolation technique that models spatial variability by estimating values at unsampled locations using a weighted average of nearby sample points. It’s used for spatial data analysis, especially in geostatistics.

– When to use: Use Kriging when dealing with spatial data where you want to estimate values at unmeasured locations while considering spatial autocorrelation.

5. Nearest Neighbor Interpolation:

– Summary: Nearest Neighbor interpolation assigns the value of the closest data point to the unknown point. It’s straightforward and is used when preserving the exact values of known data points is crucial.

– When to use: Use nearest neighbor interpolation when you want a simple method that replicates the exact values of the closest data points.

6. Bilinear Interpolation:

– Summary: Bilinear interpolation is used to estimate values in a grid by considering the weighted average of the four nearest data points. It’s commonly employed in image processing for resizing images.

– When to use: Use bilinear interpolation when you need to rescale or interpolate values within a grid or image.

7. Cubic Hermite Interpolation:

– Summary: Cubic Hermite interpolation uses cubic polynomials to approximate data points and their derivatives. It’s useful when you have both function values and derivative information at data points.

– When to use: Use cubic Hermite interpolation when you have knowledge of the derivative values at data points and want to ensure smooth transitions.

8. Radial Basis Function (RBF) Interpolation:

– Summary: RBF interpolation uses radial basis functions to interpolate data points. It’s suitable for irregularly spaced data and can capture complex non-linear relationships.

– When to use: Use RBF interpolation when you have scattered or irregularly spaced data and want to capture non-linear patterns in the data.

*Neural Networks*

Certainly! Here is a list of different neural network techniques along with a brief two-sentence summary of each technique and when to use them:

1. Feedforward Neural Networks (FNN):

– Summary: FNN, also known as artificial neural networks, consist of layers of interconnected neurons. They are used for various tasks, including regression, classification, and function approximation.

– When to use: Use FNNs for a wide range of tasks when you have labeled data and want to model complex relationships in the data.

2. Convolutional Neural Networks (CNN):

– Summary: CNNs are designed for processing grid-like data, such as images and videos. They use convolutional layers to automatically learn hierarchical features from the data.

– **When to use**: Use CNNs for tasks involving image recognition, object detection, image segmentation, and other computer vision tasks.

3. Recurrent Neural Networks (RNN):

– Summary: RNNs are specialized for sequential data and have connections that loop back on themselves, allowing them to capture temporal dependencies. They are used for tasks like time series prediction, natural language processing, and speech recognition.

– When to use: Use RNNs when dealing with sequential data, such as time series, text, or audio, and you need to model dependencies across time steps.

4. Autoencoders:

– Summary: Autoencoders are neural networks used for unsupervised learning and dimensionality reduction. They consist of an encoder and a decoder and are used for feature extraction and reconstruction tasks.

– When to use: Use autoencoders when you want to reduce the dimensionality of data, denoise it, or learn meaningful representations from unlabeled data.

7. Generative Adversarial Networks (GANs):

– Summary: GANs consist of two neural networks, a generator and a discriminator, that are trained adversarially. They are used for generating synthetic data and have applications in image synthesis, style transfer, and more.

– When to use: Use GANs when you want to generate realistic data samples that resemble the training data distribution or when you need to perform data augmentation.

8. Transformer Networks:

– Summary: Transformer networks are a type of deep learning architecture designed for sequential data processing. They use self-attention mechanisms to capture dependencies between elements in the sequence and have been highly successful in natural language processing tasks.

– When to use: Use transformer networks, such as BERT or GPT, for natural language processing tasks like text classification, translation, and sentiment analysis.

9. Radial Basis Function (RBF) Networks:

– Summary: RBF networks use radial basis functions as activation functions in their hidden layers. They are often used for function approximation and interpolation tasks.

– When to use: Use RBF networks when you need to approximate complex non-linear functions and want to leverage radial basis functions for interpolation.

*Decision Trees*

**Gradient Boosting Trees**:**Summary**: Gradient Boosting Trees, including algorithms like XGBoost, LightGBM, and CatBoost, iteratively build decision trees, emphasizing the correction of previous errors. They are highly effective for various tasks and often win machine learning competitions.**When to use**: Use Gradient Boosting Trees when you need high predictive accuracy and are willing to fine-tune hyperparameters for optimal performance.

**Random Forest**:**Summary**: Random Forest is an ensemble learning method that uses multiple decision trees and combines their predictions to improve accuracy and reduce overfitting. It’s effective for classification and regression tasks.**When to use**: Use Random Forest when you want to improve the robustness and accuracy of your decision tree model, especially in complex datasets.

**CART (Classification and Regression Trees)**:**Summary**: CART is a versatile decision tree algorithm that can be used for both classification and regression tasks. It splits data based on the most significant attribute, creating a tree structure to make predictions.**When to use**: Use CART when you have a mix of categorical and numerical data, and you want to build a decision tree for classification or regression tasks.